Solve 4sqrt{54}+4sqrt{96}

$$4 \sqrt{ 54 } +4 \sqrt{ 96 }$$

Evaluate

$$28\sqrt{6}\approx 68.585712798$$

Solution Steps

Factor 54=3^{2}\times 6. Rewrite the square root of the product \sqrt{3^{2}\times 6} as the product of square roots \sqrt{3^{2}}\sqrt{6}. Take the square root of 3^{2}.

$$4\times 3\sqrt{6}+4\sqrt{96}$$

Multiply 4 and 3 to get 12.

$$12\sqrt{6}+4\sqrt{96}$$

Factor 96=4^{2}\times 6. Rewrite the square root of the product \sqrt{4^{2}\times 6} as the product of square roots \sqrt{4^{2}}\sqrt{6}. Take the square root of 4^{2}.

$$12\sqrt{6}+4\times 4\sqrt{6}$$

Multiply 4 and 4 to get 16.

$$12\sqrt{6}+16\sqrt{6}$$

Combine 12\sqrt{6} and 16\sqrt{6} to get 28\sqrt{6}.

$$28\sqrt{6}$$